tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule

Synopsis

Usage:

eta = tensorProduct(phi,psi)

G = tensorProduct(M,V)

L = tensorProduct(L1,L2)
Inputs:
- phi, a matrix,
- psi, a matrix, representing the action of y on a sheaf on PP^1
- L1, an instance of the type VectorBundleOnE,
- L2, an instance of the type VectorBundleOnE,
- M, an instance of the type CliffordModule,
- V, an instance of the type VectorBundleOnE,
Outputs:
- eta, a matrix, action of y
- N, an instance of the type CliffordModule,
- L, an instance of the type VectorBundleOnE,

Description

Sheaves on the hyperelliptic curve y^2 -(-1)^{g}* f(s,t) are represented as sheaves on PP^1 together with the action of y. Clifford modules are represented as the action of maps eOdd_i: M_1 \to M_0 and eEv_i:M_0 \to M_1 between the even and odd parts of the module. The result are the corresponding data for the tensor product.

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : g=1

o2 = 1

i3 : (S, qq,  R,  u, M1, M2, Mu1, Mu2)=randomNicePencil(kk,g) ;

i4 : (uOdd,uEv)=cliffordOperators(Mu1,Mu2,R);

i5 : symMatrix(uOdd,uEv)

o5 = | -5t  -50s 6t     -6t  |
     | -50s 0    -9t    5t   |
     | 6t   -9t  -s-30t 3t   |
     | -6t  5t   3t     -48t |

             4      4
o5 : Matrix R  <-- R

i6 : f=det symMatrix(uOdd,uEv);

i7 : M = cliffordModule(uOdd, uEv);

i8 : L = randomLineBundle(0,f);

i9 : L.yAction

o9 = {-1} | -18s2-13st-43t2 13s2+45st-16t2 |
     {-1} | 45s2-14st-t2    18s2+13st+43t2 |

             2      2
o9 : Matrix R  <-- R

i10 : L2 = tensorProduct(L,L)

o10 = VectorBundleOnE{...1...}

o10 : VectorBundleOnE

i11 : L2.yAction

o11 = {-1} | -18s2+6st+19t2 13s2-3st-16t2 |
      {-1} | 45s2-5st+7t2   18s2-6st-19t2 |

              2      2
o11 : Matrix R  <-- R

i12 : M' = tensorProduct(M,L)

o12 = CliffordModule{...6...}

o12 : CliffordModule

i13 : M.evenCenter

o13 = {-4} | -49st-24t2 -24s2t+47st2-42t3 -10t3     -25st2-43t3   |
      {-3} | -50s       49st+24t2         -25t2     -45t2         |
      {-3} | -9t        5st+49t2          49st-17t2 50s2-15st+7t2 |
      {-3} | 5t         -2t2              24st+41t2 -49st+17t2    |

              4      4
o13 : Matrix R  <-- R

i14 : M'.evenCenter

o14 = {-4} | 47st+18t2 45s2t-33st2-27t3 24st2-11t3     -6st2+11t3      |
      {-3} | -7s+37t   -30st+7t2        34st+5t2       14st-5t2        |
      {-3} | 35s-34t   -3s2-5st-7t2     -6s2+19st-t2   -50s2-49st+43t2 |
      {-3} | -26s+50t  -36s2-37st+36t2  29s2+44st-35t2 6s2-36st-24t2   |

              4      4
o14 : Matrix R  <-- R

Ways to use tensorProduct :

tensorProduct(CliffordModule,VectorBundleOnE)
tensorProduct(Matrix,Matrix)
tensorProduct(VectorBundleOnE,VectorBundleOnE)

For the programmer

The object tensorProduct is a method function.

tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule

Synopsis

Description

See also

Ways to use tensorProduct :

For the programmer